Difference between revisions of "1965 AHSME Problems/Problem 3"
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The expression <math>(81)^{-2^{-2}}</math> has the same value as: | The expression <math>(81)^{-2^{-2}}</math> has the same value as: | ||
| − | <math>\textbf{(A)}\ \frac {1}{81} \qquad \textbf{() }\ \frac {1}{3} \qquad \textbf{(C) }\ 3 \qquad \textbf{(D) }\ 81\qquad \textbf{(E) }\ 81^4</math> | + | <math>\textbf{(A)}\ \frac {1}{81} \qquad \textbf{(B) }\ \frac {1}{3} \qquad \textbf{(C) }\ 3 \qquad \textbf{(D) }\ 81\qquad \textbf{(E) }\ 81^4</math> |
== Solution == | == Solution == | ||
We know that <math>81^{-2^{-2}}</math> is equivalent to <math>81^{\frac{1}{-2^2}}=81^{\frac{1}{4}}</math>, which is the same as <math>\sqrt[4]{81}=\boxed{3}</math>. | We know that <math>81^{-2^{-2}}</math> is equivalent to <math>81^{\frac{1}{-2^2}}=81^{\frac{1}{4}}</math>, which is the same as <math>\sqrt[4]{81}=\boxed{3}</math>. | ||
Revision as of 14:04, 23 June 2016
Problem
The expression 
has the same value as:
Solution
We know that 
is equivalent to 
, which is the same as ![$\sqrt[4]{81}=\boxed{3}$](http://latex.artofproblemsolving.com/b/b/f/bbf4a5492b809cbb628cbb14060f25cd09e04bef.png)
.
